DDMoRe Model Repository

Overview
Files
History
Model Definition
Trial Design
Modelling Steps

Short description:

Linking the population pharmacokinetics of tenofovir and its metabolites with its cellular uptake and metabolism

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Linking the population pharmacokinetics of tenofovir and its metabolites with its cellular uptake and metabolism. Madrasi K, Burns RN, Hendrix CW, Fossler MJ, Chaturvedula A CPT: pharmacometrics & systems pharmacology, 1/2014, Volume 3, pages: e147 Affiliation: Department of Pharmacy Practice, Mercer University, Atlanta, Georgia, USA. Department of Pharmaceutical Sciences, Mercer University, Atlanta, Georgia, USA. Division of Clinical Pharmacology, John Hopkins University, Baltimore, Maryland, USA. Clinical P Abstract: Empirical pharmacokinetic models are used to explain the pharmacokinetics of the antiviral drug tenofovir (TFV) and its metabolite TFV diphosphate (TFV-DP) in peripheral blood mononuclear cells. These empirical models lack the ability to explain differences between the disposition of TFV-DP in HIV-infected patients vs. healthy individuals. Such differences may lie in the mechanisms of TFV transport and phosphorylation. Therefore, we developed an exploratory model based on mechanistic mass transport principles and enzyme kinetics to examine the uptake and phosphorylation kinetics of TFV. TFV-DP median Cmax from the model was 38.5?fmol/10(6) cells, which is bracketed by two reported healthy volunteer studies (38 and 51?fmol/10(6) cells). The model presented provides a foundation for exploration of TFV uptake and phosphorylation kinetics for various routes of TFV administration and can be updated as more is known on actual mechanisms of cellular transport of TFV.
Contributors:	Paolo Magni

Context of model development:	Mechanistic Understanding;
Discrepancy between implemented model and original publication:	The model is different from the published one because for reporducing published results, according to the paper authors, the two non-linear terms in the fourth differential equations have been eliminated in the second differential equation for this hypothesis: the volume of the PBMC compartment will be small enough that transport from plasma will not impact plasma concentration. Moreover, the authors assumed that plasma transport of TFV into PBMC will be balanced by some efflux.;
Model compliance with original publication:	No;
Model implementation requiring submitter’s additional knowledge:	Yes;
Modelling context description:	Empirical pharmacokinetic models are used to explain the pharmacokinetics of the antiviral drug tenofovir (TFV) and its metabolite TFV diphosphate (TFV-DP) in peripheral blood mononuclear cells. These empirical models lack the ability to explain differences between the disposition of TFV-DP in HIV-infected patients vs. healthy individuals. Such differences may lie in the mechanisms of TFV transport and phosphorylation. Therefore, we developed an exploratory model based on mechanistic mass transport principles and enzyme kinetics to examine the uptake and phosphorylation kinetics of TFV. TFV-DP median Cmax from the model was 38.5?fmol/10(6) cells, which is bracketed by two reported healthy volunteer studies (38 and 51?fmol/10(6) cells). The model presented provides a foundation for exploration of TFV uptake and phosphorylation kinetics for various routes of TFV administration and can be updated as more is known on actual mechanisms of cellular transport of TFV.;
Modelling task in scope:	simulation;
Nature of research:	Clinical research & Therapeutic use;
Therapeutic/disease area:	Anti-infectives;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- Madrasi_2014_HIV_tenofovir.xml

Additional Files

Model owner: Paolo Magni
Submitted: Dec 13, 2015 10:16:56 AM
Last Modified: Oct 10, 2016 8:18:55 PM

Revisions

Version: 6
- Submitted on: Oct 10, 2016 8:18:55 PM
- Submitted by: Paolo Magni
- With comment: Update MDL syntax to the version 1.0 and R script to SEE version 2.0.0. Code automatically generated for NONMEM and MONOLIX
Version: 5
- Submitted on: Jul 16, 2016 5:07:39 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 2
- Submitted on: Dec 13, 2015 10:16:56 AM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.

Name

Generated from MDL. MOG ID: madrasi2004_mog

Independent Variables

Function Definitions

proportionalError : real (proportional : real, f : real) = proportional \cdot f

Parameter Model: $pm$

Random Variables

{ETA_CL}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_CL)

{ETA_V1}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_V1)

{ETA_V2}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.PPV_V2)

{EPS_Y1}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_Y1)

{EPS_Y2}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.SIGMA_Y2)

Population Parameters

POP_CL

POP_V1

POP_V2

RUV_PROP

PPV_CL

PPV_V1

PPV_V2

SIGMA_Y1

SIGMA_Y2

Individual Parameters

\ln (CL) = \ln (pm.POP_CL) + pm.ETA_CL

\ln (V1) = \ln (pm.POP_V1) + pm.ETA_V1

\ln (V2) = \ln (pm.POP_V2) + pm.ETA_V2

Structural Model: $sm$

Variables

K23 = \frac{71.41}{pm.V1}

K32 = \frac{71.41}{pm.V2}

K = \frac{pm.CL}{pm.V1}

KA = 1

FB = 0.32

KO = 0.0144375

M = 447.18

N = 45 \cdot 10^{8}

VC1 = 2.8E-13

VC2 = sm.VC1 \cdot sm.N

M1 = 287.2

M2 = 367.2

FU = 0.93

VMAX = 1.77

VU = sm.VMAX \cdot sm.FU

KM = 4.4229E-5

KCAT1 = 2.4 \cdot 3600

KM1 = 0.003

E1 = 5.6E-8

KE1 = sm.KCAT1 \cdot sm.E1

KL = 34 \cdot 10^{9}

KCAT2 = 0.12 \cdot 3600

KM2 = 2.9E-4

E2 = 2.877E-7

KE2 = sm.KCAT2 \cdot sm.E2

GSHI = 3100

GSHO = 20

GR = \frac{(sm.GSHI - sm.GSHO)}{sm.GSHO}

PA1 = \frac{sm.KE1 \cdot sm.A4}{(sm.KM1 + \frac{sm.A4}{sm.M1 \cdot sm.VC2})}

PA2 = \frac{sm.KE2 \cdot sm.A5}{(sm.KM2 + \frac{sm.A5}{sm.M2 \cdot sm.VC2})}

\begin{matrix} \frac{ⅆ}{ⅆ T} A1 = - (sm.A1 \cdot sm.KA) \\ A1 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A2 = sm.FB \cdot sm.KA \cdot sm.A1 - sm.K23 \cdot sm.A2 + sm.K32 \cdot sm.A3 - sm.K \cdot sm.A2 \\ A2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A3 = sm.K23 \cdot sm.A2 - sm.K32 \cdot sm.A3 \\ A3 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A4 = \frac{sm.VU \cdot sm.GR \cdot sm.A2}{(sm.KM + \frac{sm.FU \cdot sm.A2}{pm.V1})} - \frac{sm.VU \cdot sm.A4}{(sm.KM + \frac{sm.FU \cdot sm.A4}{sm.VC2})} - sm.KL \cdot sm.A4 - sm.PA1 \\ A4 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A5 = sm.PA1 - sm.PA2 \\ A5 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} A6 = sm.PA2 - sm.A6 \cdot sm.KO \\ A6 (T = 0) = 0 \end{matrix}

C1 = \frac{sm.A2 \cdot 10^{6}}{pm.V1}

C2 = \frac{sm.A3 \cdot 10^{6}}{pm.V2}

C3 = \frac{sm.A4 \cdot 10^{6}}{sm.VC2}

C4 = \frac{sm.A5 \cdot 10^{6}}{sm.VC2}

C5 = \frac{sm.A6 \cdot 10^{9}}{sm.M}

Observation Model: $om1$

Continuous Observation

Y1 = sm.A2 + proportionalError (proportional = pm.RUV_PROP, f = sm.A2) + pm.EPS_Y1

Observation Model: $om2$

Continuous Observation

Y2 = sm.A6 + proportionalError (proportional = pm.RUV_PROP, f = sm.A6) + pm.EPS_Y2

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_14dayMTN001.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$DOSE$	$4$	$dose$	$real$
$MDV$	$5$	$mdv$	$int$
$CMT$	$6$	$cmt$	$int$
$DVID$	$7$	$dvid$	$int$

Column Mappings

Column Ref	Modelling Mapping
$ID$	$vm_mdl.ID$
$TIME$	$T$
$DV$	${\begin{cases} om1.Y1 & if & DVID = 2 \\ om2.Y2 & if & DVID = 6 \end{cases}$
$DOSE$	${\begin{cases} sm.A1 & if & DOSE > 0 \end{cases}$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.POP_CL	$29.28$	false	$()$
pm.POP_V1	$244$	false	$()$
pm.POP_V2	$464.54$	false	$()$
pm.RUV_PROP	$1$	true	$()$
pm.PPV_CL	$0.36$	false	$()$
pm.PPV_V1	$0.79$	false	$()$
pm.PPV_V2	$0.42$	false	$()$
pm.SIGMA_Y1	$0.183$	false	$()$
pm.SIGMA_Y2	$0.567$	false	$()$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$foce$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000124: Madrasi_2014_HIV_tenofovir

Revisions

Name

Independent Variables

Function Definitions

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

Structural Model: sm

Variables

Observation Model: om1

Continuous Observation

Observation Model: om2

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Step Dependencies

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Observation Model: $om2$

Operation: $1$